ICSE

ML Aggarwal Class 7 Solutions Chapter 11 Triangles and its Properties Ex 11.5 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 11 Triangles and its Properties Ex 11.5

Question 1.
PQR is a triangle, right-angled at P. If PQ = 10 cm and PR = 24 cm, find QR.
Solution:

Question 2.
ABC is a triangle, right-angled at C. If AB = 25 cm and AC = 7 cm, find BC.
Solution:

Question 3.
Find the value of x in each of the following figures. All measurements are in centimeters.

Solution:

Question 4.
Which of the following can be the sides of a right-angled triangle?
(i) 4 cm, 5 cm, 7 cm
(ii) 1.5 cm, 2 cm, 2.5 cm
(iii) 7 cm, 5.6 cm, 4.2 cm
Solution:

Question 5.
A 15 m long ladder reaches a window 12 m high from the ground on placing it against a wall. How far is the foot of the ladder from the wall?
Solution:

Question 6.
Find the area and the perimeter of the rectangle whose length is 15 cm and the length of one diagonal is 17 cm.
Solution:

Question 7.
If the diagonals of a rhombus measure 10 cm and 24 cm, find its perimeter.
Solution:

Question 8.
The side of a rhombus is 5 cm. If the length of one diagonal of the rhombus is 8 cm, then find the length of the other diagonal.
Solution:

ML Aggarwal Class 7 Solutions Chapter 11 Triangles and its Properties Ex 11.4 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 11 Triangles and its Properties Ex 11.4

Question 1.
Is it possible to have a triangle with the following sides?
(i) 2 cm, 3 cm, 5 cm
(ii) 2.5 cm, 4.5 cm, 8 cm
(iii) 10.2 cm, 5.8 cm, 4.5 cm
(iv) 3.4 cm, 4.7 cm, 6.2 cm
Solution:

Question 2.
If the lengths of two sides of a triangle are 7 cm and 10 cm, then what can be the length of the third side?
Solution:

Question 3.
We know that in a triangle, the sum of lengths of any two sides is greater than the length of the third side. Is the sum of any angles of a triangle also greater than the third angle? If no, draw a rough sketch to show such a case.
Solution:

ML Aggarwal Class 7 Solutions Chapter 11 Triangles and its Properties Ex 11.3 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 11 Triangles and its Properties Ex 11.3

Question 1.
Find the value of x in each of the following figures:

Solution:

Question 2.
Find the value of x in each of the following figures:

Solution:

Question 3.
Find the values of x and y in each of the following figures:

Solution:

Question 4.
Calculate the size of each lettered angle in the following figures:

Solution:

Question 5.
If the angles of a triangle are in the ratio 1 : 2 : 1, find all the angles of the triangle. Classify the triangle in two different ways.
Solution:

Question 6.
In an isosceles triangle, a base angle is four times its vertical angle. Find all the angles of the triangle.
Solution:

ML Aggarwal Class 7 Solutions Chapter 11 Triangles and its Properties Ex 11.2 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 11 Triangles and its Properties Ex 11.2

Question 1.
Find the value of the unknown exterior angle x in each of the following diagrams:

Solution:

Question 2.
Find the value of the unknown interior angle x in each of the following diagrams:

Solution:

Question 3.
Find the value of x in each of the following diagrams:

Solution:

Question 4.
Find the value of unknown x in each of the following:

Solution:

Question 5.
Find the values of x and y in each of the following diagrams:

Solution:

Question 6.
Find the values of x and y in each of the following diagrams:

Solution:

Question 7.
In the adjoining figure, find the size of each lettered angle.

Solution:

Question 8.
One of the angles of a triangle measures 80° and the other two angles are equal. Find the measure of each of the equal angles.
Solution:

Question 9.
If one angle of a triangle is 60° and the other two angles are in the ratio 2 : 3, find these angles.
Solution:

Question 10.
If the angles of a triangle are in the ratio 1 : 2 : 3, find the angles. Classify the triangle in two different ways.
Solution:

Question 11.
Can a triangle have three angles whose measures are
(i) 65°, 74°, 39°?
(ii) \(\frac { 1 }{ 3 }\) right angle, 1 right angle, 60°?
Solution:

ML Aggarwal Class 7 Solutions Chapter 11 Triangles and its Properties Ex 11.1 for ICSE Understanding Mathematics acts as the best resource during your learning and helps you score well in your exams.

ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 11 Triangles and its Properties Ex 11.1

Question 1.
In the adjoining figure:

(i) Name the vertex opposite to side PQ.
(ii) Name the side opposite vertex Q.
(iii) Name the angle opposite to side QR.
(iv) Name the side opposite to ∠R.
Solution:

Question 2.
Look at the figures given below and classify each of the triangles according to its (a) sides (b) angles
(You may judge the nature of the angle by observation):

Solution:

Question 3.
In the given ∆PQR, if D is the mid-point of \(\bar { QR }\), then
(i) \(\bar { PM }\) is ……..
(ii) \(\bar { PD }\) is ………
Is QM = MR?

Solution:

Question 4.
Will an altitude always lie in the interior of a triangle? If no, draw a rough sketch to show such a case.
Solution:

Question 5.
Can you think of a triangle in which two altitudes of the triangle is its sides? If yes, draw a rough sketch to show such a case.
Solution:

Question 6.
Draw rough sketches for the following:
(i) In ∆ABC, BE is a median of the triangle.
(ii) In ∆PQR, PQ and PR are altitudes of the triangle.
(iii) In ∆XYZ, YL is an altitude in the exterior of the triangle.
Solution:

Question 7.
Take an equilateral triangle and draw its medians and altitudes and check that the medians and altitudes are the same.
Solution: